1. Field of the Invention
The present invention relates to a method for the automatic electro-chemical determination of the end point of a titration, and more particularly to such a method in which the titration agent or titrant is added to a sample in constant volume units, a value is formed by measurement after each titrant addition, the magnitude of the difference from the preceding value or step is calculated after each value formation, and, to calculate the end point V.sub.E, the three steps of greatest magnitude immediately following one another are used, with the titration ceasing when the highest step value lies between two lesser step values.
2. Description of the Prior Art
Methods of this type are described in greater detail in the periodical "Chemie-Ing.-Technik", Vol. 46, 1974, No. 19, Pages 811-817. This reference concerns the automation of potentiometric titrations. It is stated therein that sufficient significant problems result upon the evaluation of such automated titrations, that an automatic titration to an end value when given in terms of electrical potential is only possible in a few cases. The article therefore proposes to employ known methods of approximation to calculate the titration end point. These methods of approximation allow the use of simple, programmable computers. In addition, the known methods of approximation proceeds from the assumption that the end point and the turning point of the titration curve coincide. However, since the titration curve is generally not symmetrical at this point, one obtains as quotients, the three largest potential steps, (given the precondition of equi-distant titration agent additions). Appropriate equations for the approximate calculation of the end point of automated potentiometric titrations are given in Table 1 on page 813 of the said article. The inventive method, as later described, also makes use of such a known method of approximation.
As indicated in this article, the disadvantage of all of these known methods of approximation is that only three measuring points in the proximity of the end point are employed for the evaluation. It is precisely these measuring points that are typically most affected with errors caused by: the kinetics of the potential adjustment of the electrode, or the kinetics of the equilibrium adjustment regarding the chemical reaction of the titration.
Although these errors can be kept small within certain limits by the very slow addition of the titrant, this, however, results in very long titration times.
An additional significant problem which confronts the introduction of automated titrations when accomplished according to these methods of approximation occurs because the titration curve can contain more than one turning point or point of inflection and the automatic control is not able to distinguish which end point is actually the desired one.
This problem is explained in greater detail on the basis of FIG. 1 which shows a typical titration curve of an alkali in a galvanic bath being titrated with an acid, and which exhibits a second inflection point in the lower range. The titration agent additives or titrants are indicated on the abscissa axis in units of milliliters and the corresponding electrical measuring signals are indicated on the ordinate axis. These measuring signals can be proportional to the pH value. The first turning point is referenced by W1 and the second point by W2. As can be seen from the drawing, a maximum potential step .DELTA.0 already occurs at the first turning point W1, which is followed by a smaller potential step .DELTA.2 or, respectively, is preceded by a smaller potential step .DELTA.1. The first end point occurs due to the reaction of an additional bath component with the titrant, which, however, is of secondary significance for the desired titration. What is desired, however, is obtaining the second end point W2, which is characteristic for the titration of this alkali.